Universal Fault-Tolerant Quantum Computation in 2D without Getting Tied in Knots
Year: 2026
Type: article
Abstract: We show how to perform scalable fault-tolerant non-Clifford gates in two dimensions by introducing domain walls between the surface code and a non-Abelian topological code whose code space is stabilized by Clifford operators. We formulate a path-integral framework which provides both a macroscopic picture for different logical gates as well as a way to derive the associated microscopic circuits. We also show an equivalence between our approach and prior proposals where a 2D array of qubits reproduces the action of a transversal gate in a 3D stabilizer code over time, thus establishing a connection between 3D codes and 2D non-Abelian topological phases. We prove a threshold theorem for our protocols under local stochastic circuit noise using a just-in-time decoder to correct the non-Abelian code.
Source: Physical Review X
DOI: 10.1103/vrty-qs5h
Authors: Margarita Davydova, Andreas Bauer, Julio C. Magdalena de la Fuente, Mark Webster, Dominic J. Williamson, Benjamin J. Brown
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $4,200
Funders: U.S. Department of Energy, California Institute of Technology, Deutsche Forschungsgemeinschaft, Københavns Universitet, Office of Science, Walter Burke Institute for Theoretical Physics, Simons Institute for the Theory of Computing, University of California Berkeley, Institute for Quantum Information and Matter, California Institute of Technology, Engineering and Physical Sciences Research Council, Australian Research Council, Army Research Office, Army Research Laboratory
OpenAlex ID: W4415286822